Global analysis of kinetics reveals the role of secondary nucleation in recombinant spider silk self‐assembly

Abstract Recombinant spider silk proteins can be prepared in scalable fermentation processes and have been proven as sources of biomaterials for biomedical and technical applications. Nanofibrils, formed through the self‐assembly of these proteins, possess unique structural and mechanical properties, serving as fundamental building blocks for the fabrication of micro‐ and nanostructured scaffolds. Despite significant progress in utilizing nanofibrils‐based morphologies of recombinant spider silk proteins, a comprehensive understanding of the molecular mechanisms of nanofibrils self‐assembly remains a challenge. Here, a detailed kinetic study of nanofibril formation from a recombinant spider silk protein eADF4(C16) in dependence on the protein concentration, seeding, and temperature is provided. For the global fitting of kinetic data obtained during the fibril formation, we utilized the online platform AmyloFit. Evaluation of the data revealed that the self‐assembly mechanism of recombinant spider silk is dominated by secondary nucleation. Thermodynamic analyses show that both primary and secondary nucleations, as well as the elongation step of the eADF4(C16), are endothermic processes.


SUPPORTING PROCEDURES
Curve fitting using AmyloFit.
The online platform AmyloFit (www.amylofit.ch.cam.ac.uk) has been used for the global fitting of the kinetic data with the chosen model of secondary nucleation. The entire analysis was performed according to the published protocol (2). Briefly, the normalized kinetic data were uploaded to AmyloFit, which generated the half-times of eADF4(C16) aggregation. The suggesting a saturation effect. Therefore, the determination of the scaling exponent serves as a valuable first guide for selecting potential models.
In any case, the AmyloFit considers kinetic models that involve nucleation and growth processes, and it describes two quantities: the aggregate mass concentration, M(t), and the aggregate number concentration, P(t). All microscopic processes included in the kinetic models can be categorized into two groups based on whether they affect the aggregate mass or the aggregate number. The three processes considered by the authors of AmyloFit that impact the aggregate number concentration are: (i) primary nucleation, which involves homogeneous nucleation in solution and is described by a reaction order (nc) and rate constant (kn); (ii) secondary nucleation is described by the reaction order (n2) as well as the rate constant (k2), and an example is surface-catalyzed nucleation where new aggregates nucleate on the surface of existing aggregates; and (iii) fragmentation, which depends only on the concentration of aggregate mass and has reaction order 1 and a rate constant (k-). In all cases, the rate constant for elongation (k+) is considered.
One of the strengths of this platform is the capability of global fitting, also known as shared parameter fitting. This means that large datasets can be fitted simultaneously, and certain parameters such as rate constants and reaction orders can be shared among the datasets. Finally, it is important to validate the selected model through additional experiments, such as the change of the initial fibril concentration, which adds a new degree of freedom that the model has to reproduce correctly, or the addition of seeds to verify of the model of secondary nucleation.
The selected model should satisfyingly fit such additional data.
In the present study, the possible models were selected based on the linear dependence of the double logarithmic plots and the negative scaling exponents of the datasets. The reaction orders for primary (nc) and secondary nucleation (n2) were fixed across all datasets, with nc set to 2, and n2 to 1. In unseeded datasets the corresponding rate constants (k+kn and k+k2) and in seeded experiments all three rate constants (kn, k+, k2) were set as global (shared) parameters.
Using TEM images and ImageJ software (3), and considering an average protein density of 1.35 g/cm 3 (1),the average fibril length of the seeds was determined to be 495.
Subsequently, the aggregate number concentration, P0, was calculated using the formula M0/L (2) , where L represents the average fibril length. This approach was employed to minimize the degrees of freedom in the fitting procedure.
catalyze the nucleation of new aggregates from monomeric peptide, describes the entire set of time courses.
The system of secondary nucleation can be mathematically represented by the following equations [see SI-S10 and S11 of (2)